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• Riesel and Proth Prime Database
  It was created in 2007 and is maintained by [[:User:Karbon|Karsten Bonath]].
  380 bytes (59 words) - 14:14, 24 January 2019
• Primality test
  ...test for numbers less than 10000 digits, especially with the improvements by Mihailescu. But ECPP is preferred because of the certificates it provides.
  3 KB (501 words) - 05:20, 3 August 2021
• Mprime (Cray)
  '''mprime''' was the [[software]], initially authored by [[David Slowinski]] (later versions with [[Paul Gage]]), for testing [[Mers ...of very large numbers. This represented an advance over the software used by [[Landon Curt Noll]] & [[Laura A. Nickel]]. Noll had suggested the use
  639 bytes (92 words) - 12:02, 7 February 2019
• Probable prime
  ...e prime: an [[integer]] that satisfies a specific condition also satisfied by all [[prime]] numbers.}} ...ble primes have different specific conditions. While there may be probable primes that are [[Composite number|composite]] (called [[pseudoprime]]s), the cond
  2 KB (232 words) - 07:28, 12 March 2024
• GIMPS factoring and sieving
  ...mber]]s with prime exponents are eliminated from consideration as possible primes this way, so factoring is an important component of maximizing the work thr ...and furthermore must also leave a remainder of either 1 or 7 upon division by 8. See below for an explanation.
  6 KB (962 words) - 10:08, 7 March 2019
• Ten million digits
  ...of {{Num|33219281}} and higher). When first made available and handed out by [[PrimeNet]], the [[Lucas-Lehmer test]]s of these [[exponent]]s took over a ...009 a third prime greater that {{Num|10000000}} digits was found, [[M46]]. By the end of 2010, all exponents that would produce a number less than {{Num|
  979 bytes (146 words) - 14:23, 6 March 2019
• Brent-Suyama extension
  ...S=3^E where E is the product of prime powers less than B1. Then by [[Fermat's Little Theorem]], a prime number p | S-1 if p-1 | E. Slicker would be to note that all primes > 3 are of form 6k+/-1. Suppose instead that we compute T=S<sup>(6k)<sup>2<
  2 KB (421 words) - 11:51, 28 January 2019
• Self-initializing quadratic sieve
  .../math> where u is the product of small [[prime]] numbers. The set of these primes is the ''factor base''. These relations will be found using [[sieving]] as ...th> modulo any prime of the factor base. This means that about half of the primes cannot be in the factor base because <math>N</math> cannot be a [[quadratic
  10 KB (1,763 words) - 02:56, 12 March 2019
• GeneferCUDA
  It is a port of [[Genefer]] to [[CUDA]] by [[Shoichiro Yamada]]. It was also ported for AMD video cards.
  362 bytes (48 words) - 09:20, 29 January 2019
• Generalized Fermat number
  Saouter has proven that <math>F_{n,2}</math> numbers can be proven prime by using [[Pépin's test]] with k=5. In 1985, Dubner for the first time built a list of large primes of the form: b^{2^m}+1, ''b &ge; 2'' and ''m &ge; 1''.
  5 KB (759 words) - 19:04, 23 May 2024
• Worktype
  ...ain goals of GIMPS (finding [[Mersenne prime]]s, ensuring that no Mersenne primes have been missed, and lastly finding [[factor]]s for [[Mersenne number]]s). ...chine and with a different [[offset]]. Ensures that a prime was not missed by error.
  4 KB (603 words) - 02:31, 18 August 2019
• PrimeNet server
  ...s taken over by [[Aaron Blosser]], and site maintenance (''Mersenne.org'') by Aaron Blosser and [[James Heinrich]]. ...and both software packages, the range of GIMPS [[exponent]]s being handled by PrimeNet increased from [[79.3 million]] to 999,999,999.
  2 KB (381 words) - 14:05, 21 August 2019
• 100 Million Digit Prefactor Project
  ...and can be used to take exponents to a [[bit level]] higher than practical by using Prime95 alone. Factor5 can be found at: [http://www.moregimps.it/bill The project started with the introduction of 'Factor' by [[Luigi Morelli]]. It was handled using a Geocities website and e-mail. Aft
  3 KB (534 words) - 10:06, 7 March 2019
• 321 Search
  '''''This project is maintained by [[PrimeGrid]] now.''''' These are the simple steps needed to participate in the 321 Search for primes.
  1 KB (185 words) - 09:34, 3 August 2021
• Sieve of Eratosthenes
  ...be <math>2</math>. Since every second number after that will be divisible by <math>2</math>, we cross out every second number; all such numbers are comp ...ry third number which hasn't been crossed out already; these are divisible by <math>3</math> and so are composite.
  4 KB (654 words) - 11:10, 6 February 2019
• Amazon EC2
  ...al computers on which they run their own applications. The service is paid by second hence the term "elastic". Amazon EC2 instances were used to verify record-breaking primes [[M49]] and [[M50]] at the time of their discovery.
  1 KB (155 words) - 11:48, 12 February 2019
• Prime
  ...only '''prime''') is an [[integer]] greater than 1 that is only divisible by itself and 1. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19. ...dea of a 'largest prime' is fiction. And, if there is no largest prime the primes must be infinite.
  2 KB (447 words) - 00:22, 10 July 2023
• Twin prime
  ...rime''' is a [[prime|prime number]] that differs from another prime number by two, for example the twin prime pair (41, 43). ...y twin primes. But it is known that the sum of the reciprocals of all twin primes converges to Brun's constant (about 1.902160583104).
  2 KB (255 words) - 06:08, 21 February 2023
• Riesel Prime Search
  ...sel Prime Search''' (RPS) is a prime searching project established in 2005 by [[Predrag Minovic]] (Kosmaj). :# {{Vk}}-values that can produce many primes in the given range of exponent {{Vn}}
  845 bytes (120 words) - 02:21, 1 May 2024
• Seventeen or Bust/Primes
  These are the [[prime|prime numbers]] found by the [[Seventeen or Bust]] project so far. *[https://primes.utm.edu/primes/search.php All SoB primes]
  2 KB (163 words) - 14:20, 7 March 2019

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